Questions and Answers of Applied Statistics and Probability

Consider the diameter data in Exercise 15-91.(a) Construct an EWMA control chart with Î» = 0.2 and L = 3. Comment on process control.(b) Construct an EWMA control chart with
Suppose that an X̅ control chart with 2-sigma limits is used to control a process. Find the probability that a false out-of-control signal is produced on the next sample. Compare this with the
The following dataset was considered in Quality Engineering [€œAnalytic Examination of Variance Components€ (1994€“1995, Vol. 7(2)]. A quality characteristic for cement mortar briquettes
The following data from the U.S. Department of Energy Web site (www.eia.doe.gov) reported the total U.S. renewable energy consumption by year (trillion BTU) from 1973 to 2004.(a) Using all the data,
An article in Quality Engineering [€œIs the Process Capable? Tables and Graphs in Assessing Cpm€ (1992, Vol. 4(4)]. Considered manufacturing data. Specifications for the outer
Cover cases for a personal computer are manufactured by injection molding. Samples of five cases are taken from the process periodically, and the number of defects is noted. Twenty-five samples
Plastic bottles for liquid laundry detergent are formed by blow molding. Twenty samples of n = 100 bottles are inspected in time order of production, and the fraction defective in each sample is
Rework Exercise 15-91 with XÌ… and S charts.Exercise 15-91The diameter of fuse pins used in an aircraft engine application is an important quality characteristic. Twenty-five samples of
The diameter of fuse pins used in an aircraft engine application is an important quality characteristic. Twenty-five samples of three pins each are shown as follows:(a) Set up XÌ… and R
Consider the influenza data in Exercise 15-84. Use Î¼ =160 and Ïƒ = 2.(a) Construct an EWMA control chart with Î» = 0.1. Use L = 2.81. Does the process appear to be
Consider the heart rate data in Exercise 15-83. Use Î¼ = 70 and Ïƒ = 3.(a) Construct an EWMA control chart with Î» = 0.1. Use L = 2.81. Does the process appear to
The number of influenza patients (in thousands) visiting hospitals weekly is shown in the following table. Suppose that the standard deviation is Ïƒ = 2 and the target value is 160.(a)
Heart rate (in counts/minute) is measured every 30 minutes. The results of 20 consecutive measurements are as follows:Suppose that the standard deviation of the heart rate is Ïƒ = 3 and the
A process has a target of Î¼0= 100 and a standard deviation of Ïƒ = 4. Samples of size n = 1 are taken every two hours. Use Table 15-10.(a) Suppose that the process mean shifts
An early example of SPC was described in Industrial Quality Control [€œThe Introduction of Quality Control at Colonial Radio Corporation€ (1944, Vol. 1(1), pp. 4€“9)].
The PCR for a measurement is 1.5 and the control limits for an X chart with n = 4 are 24.6 and 32.6.(a) Estimate the process standard deviation σ.(b) Assume that the specification limits are
A process mean is centered between the specification limits and PCR = 1.33. Assume that the process mean increases by 1.5Ïƒ.(a) Calculate PCR and PCRk for the shifted process.(b) Calculate
A control chart for individual observations has 3-sigma control limits UCL = 1.80 and LCL = 1.62. The process specification limits are (1.64, 1.84).(a) Estimate the process standard deviation.(b)
An X control chart with 3-sigma control limits and subgroup size n = 4 has control limits UCL = 28.8 and LCL = 24.6. The process specification limits are (24, 32).(a) Estimate the process standard
Suppose that a quality characteristic is normally distributed with specifications at 150 ± 20. Natural tolerance limits for the process are 150 ± 18.(a) Calculate the process standard deviation.(b)
Suppose that a quality characteristic is normally distributed with specifications at 120 ± 20. The process standard deviation is 6.5.(a) Suppose that the process mean is 120. What are the natural
Reconsider the viscosity measurements in Exercise 15-22. The specifications are 500 ± 25. Calculate estimates of the process capability ratios PCR and PCRkfor this process and provide an
An article in Journal of the Operational Research Society [€œA Quality Control Approach for Monitoring Inventory Stock Levels,€ (1993, pp. 1115€“1127)] reported on a
An article in Quality & Safety in Health Care [€œStatistical Process Control as a Tool for Research and Healthcare Improvement,€ (2003 Vol. 12, pp. 458€“464)]
Pulsed laser deposition technique is a thin film deposition technique with a high-powered laser beam. Twenty-five films were deposited through this technique. The thicknesses of the films obtained
The following table of data was analyzed in Quality Engineering [1991€“1992, Vol. 4(1)]. The average particle size of raw material was obtained from 25 successive samples.(a) Using all the
The viscosity of a chemical intermediate is measured every hour. Twenty samples each of size n = 1 are in the following table.(a) Using all the data, compute trial control limits for individual
An automatic sensor measures the diameter of holes in consecutive order. The results of measuring 25 holes are in the following table.(a) Using all the data, compute trial control limits for
In a semiconductor manufacturing process, CVD metal thickness was measured on 30 wafers obtained over approximately two weeks. Data are shown in the following table.(a) Using all the data, compute
The thickness of a metal part is an important quality parameter. Data on thickness (in inches) are given in the following table, for 25 samples of five parts each.(a) Using all the data, find trial
An extrusion die is used to produce aluminum rods. The diameter of the rods is a critical quality characteristic. The following table shows xÌ… and r values for 20 samples of five rods each.
An X̅ control chart with three-sigma control limits has UCL = 48.75 and LCL = 42.71. Suppose that the process standard deviation is σ = 2.25. What subgroup size was used for the chart?
The level of cholesterol (in mg/dL) is an important index for human health. The sample size is n = 5. The following summary statistics are obtained from cholesterol measurements:(a) Find trial
Samples of size n = 6 are collected from a process every hour. After 20 samples have been collected, we calculate x̅̅ = 20.0 and r̅ / d2 = 1.4.(a) Calculate trial control limits for X and R
Control charts are to be constructed for samples of size n = 4, and xÌ… and s are computed for each of 20 preliminary samples as follows:(a) Calculate trial control limits for
Twenty-five samples of size 5 are drawn from a process at one-hour intervals, and the following data are obtained:(a) Calculate trial control limits for XÌ… and R charts.(b) Repeat part
Control charts for XÌ… and R are to be set up for an important quality characteristic. The sample size is n = 5, and xÌ… and r are computed for each of 35 preliminary samples.
Show that can express the residuals from a multiple regression model as e =−(I - H)y where H = X(X X)-1 X'.
A regression model is used to relate a response to k = 4 regressors with n = 20. What is the smallest value of R2 that will result in a significant regression if α = 0.05? Use the results of the
Consider a multiple regression model with k regressors. Show that the test statistic for significance of regression can be written as Suppose that n = 20, k = 4, and R2 = 090. If Î± = 0.05,
Consider the following inverse model matrix.
Exercise 12-9 introduced the hospital patient satisfaction survey data. One of the variables in that data set is a categorical variable indicating whether the patient is a medical patient or a
A multiple regression model was used to relate y = viscosity of a chemical product to x1 = temperature and x2 = reaction time. The data set consisted of n = 15 observations.(a) The estimated
An article in IEEE Transactions on Instrumentation and Measurement (2001, Vol. 50, pp. 2033€“2040) reported on a study that had analyzed powdered mixtures of coal and limestone for
An article in Cancer Epidemiology, Biomarkers and Prevention (1996, Vol. 5, pp. 849€“852) reported on a pilot study to assess the use of toenail arsenic concentrations as an indicator of
Table E12-3 provides the highway gasoline mileage test results for 2005 model year vehicles from DaimlerChrysler.The full table of data (available on the book€™s Web site) contains the same
Consider the following inverse of the model matrix:
Consider the following computer output.(a) Fill in the missing values. Use bounds for the P-values.(b) Is the overall model significant at Î± = 0.05? Is it significant at Î±
Consider the gas mileage data in Exercise 12-11. Build regression models for the data from the numerical regressors using the following techniques:(a) All possible regressions.(b) Stepwise
Consider the arsenic data in Exercise 12-16. Use arsenic in nails as the response and age, drink use, and cook use as the regressors. Build regression models for the data using the following
Use the football data in Exercise 12-21 to build regression models using the following techniques:(a) All possible regressions. Find the equations that minimize MSE and that minimize Cp.(b) Stepwise
Consider the stack loss data in Exercise 12-20. Build regression models for the data using the following techniques:(a) All possible regressions.(b) Stepwise regression.(c) Forward selection.(d)
Consider the nisin extraction data in Exercise 12-18. Build regression models for the data using the following techniques:(a) All possible regressions.(b) Stepwise regression.(c) Forward
Consider the gray range modulation data in Exercise 12-19. Use the useful range as the response. Build regression models for the data using the following techniques:(a) All possible regressions.(b)
Consider the regression model fit to the coal and limestone mixture data in Exercise 12-17. Use density as the response. Build regression models for the data using the following techniques:(a) All
Consider the X-ray inspection data in Exercise 12-15.Use rads as the response. Build regression models for the data using the following techniques:(a) All possible regressions.(b) Stepwise
Consider the arsenic concentration data in Exercise 12-16.(a) Discuss how you would model the information about the person€™s sex.(b) Fit a regression model to the arsenic in nails using
Consider the stack loss data in Exercise 12-20.(a) What proportion of total variability is explained by this model?(b) Construct a normal probability plot of the residuals. What conclusion can you
Consider the regression model fit to the gray range modulation data in Exercise 12-19. Use the useful range as the response.(a) What proportion of total variability is explained by this model?(b)
Consider the regression model fit to the nisin extraction data in Exercise 12-18.(a) What proportion of total variability is explained by this model?(b) Construct a normal probability plot of the
Consider the regression model fit to the coal and limestone mixture data in Exercise 12-17. Use density as the response.(a) What proportion of total variability is explained by this model?(b)
Consider the regression model fit to the arsenic data in Exercise 12-16. Use arsenic in nails as the response and age, drink use, and cook use as the regressors.(a) What proportion of total
Consider the regression model fit to the X-ray inspection data in Exercise 12-15. Use rads as the response.(a) What proportion of total variability is explained by this model?(b) Construct a normal
Consider the NFL data in Exercise 12-21.(a) Find 95% confidence intervals on the regression coefficients.(b) What is the estimated standard error of μ̂Y|x0 when the percentage of completions is
Consider the stack loss data in Exercise 12-20.(a) Calculate 95% confidence intervals on each regression coefficient.(b) Calculate a 95% confidence interval on mean stack loss when x1 = 80, x2 = 25
Consider the regression model fit to the gray range modulation data in Exercise 12-19. Use the useful range as the response.(a) Calculate 99% confidence intervals on each regression coefficient.(b)
Consider the regression model fit to the nisin extraction data in Exercise 12-18.(a) Calculate 95% confidence intervals on each regression coefficient.(b) Calculate a 95% confidence interval on mean
Consider the regression model fit to the coal and limestone mixture data in Exercise 12-17. Use density as the response.(a) Calculate 90% confidence intervals on each regression coefficient.(b)
Consider the regression model fit to the arsenic data in Exercise 12-16. Use arsenic in nails as the response and age, drink use, and cook use as the regressors.(a) Calculate 99% confidence intervals
Consider the regression model fit to the X-ray inspection data in Exercise 12-15. Use rads as the response.(a) Calculate 95% confidence intervals on each regression coefficient.(b) Calculate a 99%
Consider the regression model fit to the shear strength of soil in Exercise 12-5.(a) Calculate 95% confidence intervals on each regression coefficient.(b) Calculate a 95% confidence interval on mean
Use the second-order polynomial regression model from Exercise 12-4,(a) Find a 95% confidence interval on both the first-order and the second-order term in this model.(b) Is zero in the confidence
Referring to the regression model from Exercise 12-3,(a) Find a 95% confidence interval for the coefficient of spending on higher education.(b) Is zero in the confidence interval you found in part
Using the regression from Exercise 12-2,(a) Find a 95% confidence interval for the coefficient of hourly 1 test.(b) Find a 95% confidence interval for the mean final grade for students who score 80
Using the regression model from Exercise 12-1,(a) Find a 95% confidence interval for the coefficient of height.(b) Find a 95% confidence interval for the mean percent of body fat for a man with a
Data from a hospital patient satisfaction survey were presented in Exercise 12-9.(a) Fit a regression model using only the patient age and severity regressors. Test the model from this exercise for
Data from a hospital patient satisfaction survey were presented in Exercise 12-9.(a) Test the model from this exercise for significance of regression. What conclusions can you draw if Î±
Consider the bearing wear data in Exercise 12-23.(a) For the model with no interaction, test for significance of regression using Î± = 0.05. What is the P-value for this test? What are
Exercise 12-2 presented a regression model to predict final grade from two hourly tests.(a) Test the hypotheses that each of the slopes is zero.(b) What is the value of R2 for this model?(c) What is
Constrained Least Squares. Suppose we wish to find the least squares estimator of a in the model y = XÎ² + Îµ subject to a set of equality constraints, say, TÎ² =
Consider the multiple linear regression model y = Xβ + ε. If β adenotes the least squares estimator of β, show that β = β + Re, where (X'X)-1 X'.
You have fit a regression model with two regressors to a data set that has 20 observations. The total sum of squares is 1000 and the model sum of squares is 750.(a) What is the value of R2 for this
An article in Technometrics (1974, Vol. 16, pp. 523€“531) considered the following stack-loss data from a plant oxidizing ammonia to nitric acid. Twenty-one daily responses of stack loss
Consider the NFL data in Exercise 12-21.(a) Test for significance of regression using Î± = 0.05. What is the P-value for this test?(b) Conduct the t-test for each regression coefficient.
Consider the regression model fit to the stack loss data in Exercise 12-20. Use stack loss as the response.(a) Test for significance of regression using Î± = 0.05. What is the P-value
Consider the regression model fit to the gray range modulation data in Exercise 12-19. Use the useful range as the response.(a) Test for significance of regression using Î± = 0.05. What
Consider the regression model fit to the nisin extraction data in Exercise 12-18. Use nisin extraction as the response.(a) Test for significance of regression using Î± = 0.05. What is
Consider the regression model fit to the X-ray inspection data in Exercise 12-15. Use rads as the response.(a) Test for significance of regression using α = 0.05. What is the P-value for this
Consider the regression model fit to the arsenic data in Exercise 12-16. Use arsenic in nails as the response and age, drink use, and cook use as the regressors.(a) Test for significance of
Consider the following computer output.(a) Fill in the missing quantities. You may use bounds for the P-values.(b) What conclusions can you draw about the significance of regression?(c) What
Consider the linear regression model from Exercise 12-4. Is the second-order term necessary in the regression model?Exercise 12-4Hsuie, Ma, and Tsai (€˜€˜Separation and
Consider the regression model of Exercise 12-3 attempting to predict the percent of engineers in the workforce from various spending variables.(a) Are any of the variables useful for prediction?
Exercise 12-2 presented a regression model to predict final grade from two hourly tests.(a) Test the hypotheses that each of the slopes is zero.(b) What is the value of R2 for this model?(c) What is
Recall the regression of percent of body fat on height and waist from Exercise 12-1. The simple regression model of percent of body fat on height alone shows the following:(a) Test whether the
Table E12-12 presents statistics for the National Hockey League teams from the 2008€“2009 season (The Sports Network). Fit a multiple linear regression model that relates wins to the
Table E12-11 presents quarterback ratings for the 2008 National Football League season (The Sports Network). (a) Fit a multiple regression model to relate the quarterback rating to the
An article in Optical Engineering [€œOperating Curve Extraction of a Correlator€™s Filter€ (2004, Vol. 43, pp. 2775€“2779)] reported on the use of an optical
An article in Biotechnology Progress (2001, Vol. 17, pp. 366€“368) reported on an experiment to investigate and optimize nisin extraction in aqueous two-phase systems (ATPS). The nisin
An article in IEEE Transactions on Instrumentation and Measurement (2001, Vol. 50, pp. 2033€“2040) reported on a study that had analyzed powdered mixtures of coal and limestone for
An article in Cancer Epidemiology, Biomarkers and Prevention (1996, Vol. 5, pp. 849€“852) reported on a pilot study to assess the use of toenail arsenic concentrations as an indicator of

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